Advanced Lane Finding Project¶
The goals / steps of this project are the following:
- Compute the camera calibration matrix and distortion coefficients given a set of chessboard images.
- Apply a distortion correction to raw images.
- Use color transforms, gradients, etc., to create a thresholded binary image.
- Apply a perspective transform to rectify binary image ("birds-eye view").
- Detect lane pixels and fit to find the lane boundary.
- Determine the curvature of the lane and vehicle position with respect to center.
- Warp the detected lane boundaries back onto the original image.
- Output visual display of the lane boundaries and numerical estimation of lane curvature and vehicle position.
First, I'll compute the camera calibration using chessboard images¶
In [1]:
import numpy as np
import cv2
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
import glob
%matplotlib inline
camera_model = None
In [2]:
class CameraModel():
'''
Class to represent the camera model. Provides function for undistoring image
'''
def __init__(self, calibration_images):
'''
calibration_images - list of paths to calibration images
'''
mtx, dist = self._calibrate_camera(calibration_images)
self._camera_matrix = mtx
self._distortion = dist
def undistort(self, image):
'''
takes an image and returns an undistorted copy
image - the image to undistort
'''
return cv2.undistort(image, self._camera_matrix, self._distortion, None, self._camera_matrix)
def _calibrate_camera(self, calibration_images):
'''
Computes the camera intrinsics and extrinsics.
calibration_images - list of paths to calibration images
'''
objpoints = [] # 3d points in real world space
imgpoints = [] # 2d points in image plane
nx = 9 # num corners on the x axis
ny = 6 # num corners on the y axis
# Prepare object points: (0,0,0), (1,0,0), (2,0,0) ... (8,5,0)
objp = np.zeros((ny * nx, 3), np.float32)
objp[:,:2] = np.mgrid[0:nx, 0:ny].T.reshape(-1, 2) # gen x,y coordinates
for file in calibration_images:
img = mpimg.imread(file)
gray = cv2.cvtColor(img, cv2.COLOR_RGB2GRAY)
ret, corners = cv2.findChessboardCorners(gray, (nx, ny), None)
if ret:
imgpoints.append(corners)
objpoints.append(objp)
else:
print("Failed to find corners in", file)
# Now use calibrate camera to get the intrinsics (and ignore extrinsics)
ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(objpoints, imgpoints, gray.shape[::-1], None, None)
return mtx, dist
cal_images = glob.glob('./camera_cal/calibration*.jpg')
if camera_model is None:
camera_model = CameraModel(cal_images)
# Now test the distortion
test_image = mpimg.imread('./camera_cal/calibration1.jpg')
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(20, 10))
fig.tight_layout()
ax1.imshow(test_image)
ax1.set_title('Original Image')
ax2.imshow(camera_model.undistort(test_image))
ax1.set_title('Undistorted Image')
Out[2]:
In [3]:
assert(camera_model is not None)
Create Thresholded Binary Image¶
In [4]:
def threshold_image(img, s_thresh=(170, 255), sx_thresh=(20, 100)):
'''
takes an image and returns a thresholded binary image that best accentuates
the lanes in the image. Uses a sobel operation with respect to x on a grayscale
version of the image and binary ors it with the a thresholded S-channel from an HLS
copy of the image.
img - the image to process
s_thresh - thesholds for the S channel of the HLS space
sx_thresh - thresholds for the sobel operation in the x direction
'''
img = np.copy(img)
# Convert to HSV color space and separate the V channel
hls = cv2.cvtColor(img, cv2.COLOR_RGB2HLS).astype(np.float)
s_channel = hls[:,:,2]
# Sobel x
gray = cv2.cvtColor(img, cv2.COLOR_RGB2GRAY)
sobelx = cv2.Sobel(gray, cv2.CV_64F, 1, 0) # Take the derivative in x
abs_sobelx = np.absolute(sobelx) # Absolute x derivative to accentuate lines away from horizontal
scaled_sobel = np.uint8(255 * abs_sobelx / np.max(abs_sobelx))
# Threshold x gradient
sxbinary = np.zeros_like(scaled_sobel)
sxbinary[(scaled_sobel >= sx_thresh[0]) & (scaled_sobel <= sx_thresh[1])] = 1
# Threshold color channel
s_binary = np.zeros_like(s_channel)
s_binary[(s_channel >= s_thresh[0]) & (s_channel <= s_thresh[1])] = 1
combined_binary = np.zeros_like(s_channel)
combined_binary[(s_binary == 1) | (sxbinary == 1)] = 1
return combined_binary
test_image_filenames = glob.glob('./test_images/*.jpg')
test_images = [camera_model.undistort(mpimg.imread(img)) for img in test_image_filenames]
results = [threshold_image(img) for img in test_images]
# Plot the result
f, axes = plt.subplots(len(results), 2, figsize=(24, 70))
f.tight_layout()
for i in range(len(test_images)):
ax1 = axes[i][0]
ax1.imshow(test_images[i])
ax1.set_title('Original Image', fontsize=40)
ax2 = axes[i][1]
ax2.imshow(results[i], cmap='gray')
ax2.set_title('Pipeline Result', fontsize=40)
plt.subplots_adjust(left=0., right=1, top=0.9, bottom=0.)
Perspective Transform¶
In [5]:
from numpy.linalg import inv
def get_perspective_transform_funcs():
'''
Creates and returns two functions for applying a perspective transform and
reversing it.
'''
# src and dst points found externally. Used to compute the perspective
# transform.
src = np.float32([[582, 460], [702, 460], [1100, 719], [205, 719]])
dst = np.float32([[313, 200], [941, 200], [941, 719], [313, 719]])
M = cv2.getPerspectiveTransform(src, dst)
Minv = inv(M)
def apply_perspective_transform(img):
'''
Takes an image and performs a perspective transformation
'''
height, width = img.shape[:2]
return cv2.warpPerspective(img, M, (width, height), flags=cv2.INTER_LINEAR)
def apply_reverse_transform(img):
'''
Takes an image and performs a perspective transformation
'''
# Warp the blank back to original image space using inverse perspective matrix (Minv)
return cv2.warpPerspective(img, Minv, (img.shape[1], img.shape[0]))
return apply_perspective_transform, apply_reverse_transform
# get the transformation functions
transform_perspective, reverse_transform_perspective = get_perspective_transform_funcs()
def load_and_transform_image(filename):
'''
takes a file path to an image, loads it, undistorts it, theholds it,
and then performs a perspective transform on it to give an over-head view.
returns: original image, undistorted image, binary thresholded image, perspective-transformed image
'''
orig = mpimg.imread(filename)
undist = camera_model.undistort(orig)
binary = threshold_image(undist)
binary_warped = transform_perspective(binary)
return orig, undist, binary, binary_warped
orig, undist, binary, binary_warped = load_and_transform_image('./test_images/straight_lines1.jpg')
f, ((ax1, ax2), (ax3, ax4), (ax5, ax6)) = plt.subplots(3, 2, figsize=(24, 30))
x = [582, 702, 1100, 205, 582]
y = [460, 460, 719, 719, 460]
left_line_x = 313
right_line_x = 941
f.tight_layout()
ax1.imshow(undist)
ax1.plot(x, y, color='red')
ax1.set_title('Original Image', fontsize=50)
ax2.imshow(binary_warped, cmap="gray")
ax2.set_title('Undistorted and warped', fontsize=50)
ax2.axvline(left_line_x, color='red')
ax2.axvline(right_line_x, color='red')
orig, undist, binary, binary_warped = load_and_transform_image('./test_images/straight_lines2.jpg')
ax3.imshow(undist)
ax3.plot(x, y, color='red')
ax3.set_title('Original Image', fontsize=50)
ax4.imshow(binary_warped, cmap="gray")
ax4.set_title('Undistorted and warped', fontsize=50)
ax4.axvline(left_line_x, color='red')
ax4.axvline(right_line_x, color='red')
orig, undist, binary, binary_warped = load_and_transform_image('./test_images/test1.jpg')
ax5.imshow(undist)
ax5.plot(x, y, color='red')
ax5.set_title('Original Image', fontsize=50)
ax6.imshow(binary_warped, cmap="gray")
ax6.set_title('Undistorted and warped', fontsize=50)
ax6.axvline(left_line_x, color='red')
ax6.axvline(right_line_x, color='red')
plt.subplots_adjust(left=0., right=1, top=0.9, bottom=0.)
Detect and draw lanes¶
In [6]:
orig, undist, binary, binary_warped = load_and_transform_image('./test_images/straight_lines1.jpg')
histogram = np.sum(binary_warped[binary_warped.shape[0]//2:,:], axis=0)
plt.plot(histogram)
plt.imshow(binary_warped, cmap='gray')
Out[6]:
In [7]:
def detect_lines_cached(binary_warped, left_fit, right_fit):
'''
Detects lane lines in an image - assumes that you have previously detected
lane lines, and are providing the polynomials for the previous lines. Uses
that information to better inform the search in the new image
binary_warped - new image to search for lane line in
left_fit - polynomial coefficients for the previous left lane line
right_fit - polynomial coefficients for the previous right lane line
returns: y values for points, x values for left line, x values for right line,
left polynomial coefficients, right polynomial coefficients
'''
# Assume you now have a new warped binary image
# from the next frame of video (also called "binary_warped")
# It's now much easier to find line pixels!
nonzero = binary_warped.nonzero()
nonzeroy = np.array(nonzero[0])
nonzerox = np.array(nonzero[1])
margin = 100
left_lane_inds = ((nonzerox > (left_fit[0]*(nonzeroy**2) + left_fit[1]*nonzeroy + left_fit[2] - margin)) & (nonzerox < (left_fit[0]*(nonzeroy**2) + left_fit[1]*nonzeroy + left_fit[2] + margin)))
right_lane_inds = ((nonzerox > (right_fit[0]*(nonzeroy**2) + right_fit[1]*nonzeroy + right_fit[2] - margin)) & (nonzerox < (right_fit[0]*(nonzeroy**2) + right_fit[1]*nonzeroy + right_fit[2] + margin)))
# Again, extract left and right line pixel positions
leftx = nonzerox[left_lane_inds]
lefty = nonzeroy[left_lane_inds]
rightx = nonzerox[right_lane_inds]
righty = nonzeroy[right_lane_inds]
# Fit a second order polynomial to each
left_fit = np.polyfit(lefty, leftx, 2)
right_fit = np.polyfit(righty, rightx, 2)
# Generate x and y values for plotting
ploty = np.linspace(0, binary_warped.shape[0]-1, binary_warped.shape[0] )
left_fitx = left_fit[0]*ploty**2 + left_fit[1]*ploty + left_fit[2]
right_fitx = right_fit[0]*ploty**2 + right_fit[1]*ploty + right_fit[2]
return ploty, left_fitx, right_fitx, left_fit, right_fit
def detect_lines(binary_warped, draw=False):
'''
Detects lane lines in an image
binary_warped - new image to search for lane line in
draw - bool - whether or not to plot the lane lines
returns: y values for points, x values for left line, x values for right line,
left polynomial coefficients, right polynomial coefficients
'''
# Assuming you have created a warped binary image called "binary_warped"
# Take a histogram of the bottom half of the image
histogram = np.sum(binary_warped[binary_warped.shape[0]//2:,:], axis=0)
# Create an output image to draw on and visualize the result
out_img = np.dstack((binary_warped, binary_warped, binary_warped))*255
# Find the peak of the left and right halves of the histogram
# These will be the starting point for the left and right lines
midpoint = np.int(histogram.shape[0]/2)
leftx_base = np.argmax(histogram[:midpoint])
rightx_base = np.argmax(histogram[midpoint:]) + midpoint
# Choose the number of sliding windows
nwindows = 9
# Set height of windows
window_height = np.int(binary_warped.shape[0]/nwindows)
# Identify the x and y positions of all nonzero pixels in the image
nonzero = binary_warped.nonzero()
nonzeroy = np.array(nonzero[0])
nonzerox = np.array(nonzero[1])
# Current positions to be updated for each window
leftx_current = leftx_base
rightx_current = rightx_base
# Set the width of the windows +/- margin
margin = 100
# Set minimum number of pixels found to recenter window
minpix = 50
# Create empty lists to receive left and right lane pixel indices
left_lane_inds = []
right_lane_inds = []
# Step through the windows one by one
for window in range(nwindows):
# Identify window boundaries in x and y (and right and left)
win_y_low = binary_warped.shape[0] - (window+1)*window_height
win_y_high = binary_warped.shape[0] - window*window_height
win_xleft_low = leftx_current - margin
win_xleft_high = leftx_current + margin
win_xright_low = rightx_current - margin
win_xright_high = rightx_current + margin
# Draw the windows on the visualization image
cv2.rectangle(out_img,(win_xleft_low,win_y_low),(win_xleft_high,win_y_high),(0,255,0), 2)
cv2.rectangle(out_img,(win_xright_low,win_y_low),(win_xright_high,win_y_high),(0,255,0), 2)
# Identify the nonzero pixels in x and y within the window
good_left_inds = ((nonzeroy >= win_y_low) & (nonzeroy < win_y_high) & (nonzerox >= win_xleft_low) & (nonzerox < win_xleft_high)).nonzero()[0]
good_right_inds = ((nonzeroy >= win_y_low) & (nonzeroy < win_y_high) & (nonzerox >= win_xright_low) & (nonzerox < win_xright_high)).nonzero()[0]
# Append these indices to the lists
left_lane_inds.append(good_left_inds)
right_lane_inds.append(good_right_inds)
# If you found > minpix pixels, recenter next window on their mean position
if len(good_left_inds) > minpix:
leftx_current = np.int(np.mean(nonzerox[good_left_inds]))
if len(good_right_inds) > minpix:
rightx_current = np.int(np.mean(nonzerox[good_right_inds]))
# Concatenate the arrays of indices
left_lane_inds = np.concatenate(left_lane_inds)
right_lane_inds = np.concatenate(right_lane_inds)
# Extract left and right line pixel positions
leftx = nonzerox[left_lane_inds]
lefty = nonzeroy[left_lane_inds]
rightx = nonzerox[right_lane_inds]
righty = nonzeroy[right_lane_inds]
# Fit a second order polynomial to each
left_fit = np.polyfit(lefty, leftx, 2)
right_fit = np.polyfit(righty, rightx, 2)
# Generate x and y values for plotting
ploty = np.linspace(0, binary_warped.shape[0]-1, binary_warped.shape[0] )
left_fitx = left_fit[0]*ploty**2 + left_fit[1]*ploty + left_fit[2]
right_fitx = right_fit[0]*ploty**2 + right_fit[1]*ploty + right_fit[2]
#out_img[nonzeroy[left_lane_inds], nonzerox[left_lane_inds]] = [255, 0, 0]
#out_img[nonzeroy[right_lane_inds], nonzerox[right_lane_inds]] = [0, 0, 255]
if draw:
plt.imshow(out_img)
plt.plot(left_fitx, ploty, color='yellow')
plt.plot(right_fitx, ploty, color='yellow')
plt.xlim(0, 1280)
plt.ylim(720, 0)
return ploty, left_fitx, right_fitx, left_fit, right_fit
def calc_curvature(img_shape, ploty, left_fitx, right_fitx, left_fit, right_fit):
'''
Calculates the curvature of the lines in world space and the deviation from
the center of the lane.
Returns: left lane radius of curvature in meters, right lane radius of curvature in meters,
deviation from the center of the lane in meters.
'''
# Now calc curvature
y_eval = np.max(ploty)
left_curverad = ((1 + (2*left_fit[0]*y_eval + left_fit[1])**2)**1.5) / np.absolute(2*left_fit[0])
right_curverad = ((1 + (2*right_fit[0]*y_eval + right_fit[1])**2)**1.5) / np.absolute(2*right_fit[0])
# Define conversions in x and y from pixels space to meters
ym_per_pix = 30/720 # meters per pixel in y dimension
xm_per_pix = 3.7/700 # meters per pixel in x dimension
# Fit new polynomials to x,y in world space
left_fit_cr = np.polyfit(ploty*ym_per_pix, left_fitx*xm_per_pix, 2)
right_fit_cr = np.polyfit(ploty*ym_per_pix, right_fitx*xm_per_pix, 2)
# Calculate the new radii of curvature
left_curverad = ((1 + (2*left_fit_cr[0]*y_eval*ym_per_pix + left_fit_cr[1])**2)**1.5) / np.absolute(2*left_fit_cr[0])
right_curverad = ((1 + (2*right_fit_cr[0]*y_eval*ym_per_pix + right_fit_cr[1])**2)**1.5) / np.absolute(2*right_fit_cr[0])
img_height = img_shape[0] * ym_per_pix
img_width = img_shape[1] * xm_per_pix
left = left_fit_cr[0] * img_height ** 2 + left_fit_cr[1] * img_height + left_fit_cr[2]
right = right_fit_cr[0] * img_height ** 2 + right_fit_cr[1] * img_height + right_fit_cr[2]
center = (left + right) / 2.0
off_center = (center - img_width / 2.0)
# Now our radius of curvature is in meters
return left_curverad, right_curverad, off_center
orig, undist, binary, binary_warped = load_and_transform_image('./test_images/straight_lines1.jpg')
ploty, left_fitx, right_fitx, left_fit, right_fit = detect_lines(binary_warped, draw=True)
print(calc_curvature(undist.shape, ploty, left_fitx, right_fitx, left_fit, right_fit))
In [8]:
from numpy.linalg import inv
def draw_overlay(undist, ploty, left_fitx, right_fitx, plot=True):
'''
draws an overlay onto the provided image highlighting the lane
undist - undistorted image of the road to draw the lane on top of
ploty - y values for lanes
left_fitx - x values for left line
right_fitx - x values for right line
left_fit - polynomial coefficients for the previous left lane line
right_fit - polynomial coefficients for the previous right lane line
returns: image with lanes overlay
'''
# Create an image to draw the lines on
warp_zero = np.zeros_like(binary).astype(np.uint8)
color_warp = np.dstack((warp_zero, warp_zero, warp_zero))
# Recast the x and y points into usable format for cv2.fillPoly()
pts_left = np.array([np.transpose(np.vstack([left_fitx, ploty]))])
pts_right = np.array([np.flipud(np.transpose(np.vstack([right_fitx, ploty])))])
pts = np.hstack((pts_left, pts_right))
# Draw the lane onto the warped blank image
cv2.fillPoly(color_warp, np.int_([pts]), (0, 255, 0))
newwarp = reverse_transform_perspective(color_warp)
# Combine the result with the original image
result = cv2.addWeighted(undist, 1, newwarp, 0.3, 0)
if plot:
plt.imshow(result)
return result
_ = draw_overlay(undist, ploty, left_fitx, right_fitx)
Putting it all together¶
In [9]:
left_fit = None
right_fit = None
def process_image(orig):
'''
Takes an distorted image and returns an undistorted image with lanes overlaid
'''
global left_fit, right_fit
undist = camera_model.undistort(orig)
binary = threshold_image(undist)
binary_warped = transform_perspective(binary)
if left_fit is not None and right_fit is not None:
ploty, left_fitx, right_fitx, left_fit, right_fit = detect_lines_cached(binary_warped, left_fit, right_fit)
else:
ploty, left_fitx, right_fitx, left_fit, right_fit = detect_lines(binary_warped)
result = draw_overlay(undist, ploty, left_fitx, right_fitx, plot=False)
left_curv, right_curv, off_center = calc_curvature(undist.shape, ploty, left_fitx, right_fitx, left_fit, right_fit)
curve_text = "Curvature: Left = {:.2f}, Right = {:.2f}".format(left_curv, right_curv)
font = cv2.FONT_HERSHEY_SIMPLEX
cv2.putText(result, curve_text, (20, 50), font, 1, (0,255,0), 2)
off_center_text = "Deviation from center = {:.2f} m".format(off_center)
cv2.putText(result, off_center_text, (20, 80), font, 1, (0,255,0), 2)
return result
def process_image_file(filename):
'''
Takes a path to a distorted image and plots an undistorted image with lanes overlaid
'''
orig, undist, binary, binary_warped = load_and_transform_image(filename)
ploty, left_fitx, right_fitx, left_fit, right_fit = detect_lines(binary_warped)
left_curv, right_curv, off_center = calc_curvature(undist.shape, ploty, left_fitx, right_fitx, left_fit, right_fit)
curve_text = "Curvature: Left = {:.2f}m, Right = {:.2f}m".format(left_curv, right_curv)
font = cv2.FONT_HERSHEY_SIMPLEX
cv2.putText(undist, curve_text, (20, 50), font, 1, (0,255,0), 2)
off_center_text = "Deviation from center = {:.2f}m".format(off_center)
cv2.putText(undist, off_center_text, (20, 80), font, 1, (0,255,0), 2)
draw_overlay(undist, ploty, left_fitx, right_fitx)
process_image_file('./test_images/test5.jpg')
Running on videos¶
In [10]:
# Import everything needed to edit/save/watch video clips
from moviepy.editor import VideoFileClip
from IPython.display import HTML
output = 'output.mp4'
clip1 = VideoFileClip("project_video.mp4")
clip = clip1.fl_image(process_image) #NOTE: this function expects color images!!
%time clip.write_videofile(output, audio=False)
In [11]:
HTML("""
<video width="960" height="540" controls>
<source src="{0}">
</video>
""".format(output))
Out[11]: